Hidden charmonium decays of spin-2 partner of $X(3872)$

Abstract

The Belle collaboration recently reported a promising candidate for the spin-2 $D^{\ast }{\bar{D}}^{\ast }$ partner of the $X(3872)$, called the $X_2$ for short, having a mass of $(4014.3\pm 4.0\pm 1.5)\mathrm{MeV}$ and a width of $(4\pm 11\pm 6)\mathrm{MeV}$. Assuming the $X_2$ as a pure molecule of the $D^{\ast }{\bar{D}}^{\ast }$, we calculated in detail the hidden charmonium decays of the $X_2\to J/\psi V$ and $X_2\to {\eta }_{c}P$ via the intermediate meson loops, where $V={\rho }^0,\omega$ and $P={\pi }^0,\eta ,{\eta }^{\prime }$. The results indicate that the decay widths are strongly dependent on the $X_2$ mass. At present center value of the mass $4014.3\mathrm{MeV}$, the width for the $X_2\to J/\psi {\rho }^0$ is predicted to be a few tens of keV, while it is on the order of $10^{2\text{-}3}\mathrm{keV}$ for the $X_2\to J/\psi \omega$; the predicted width for the $X_2\to {\eta }_c{\pi }^0$ is about a few keV, while the widths for $X_2\to {\eta }_c\eta$ and ${\eta }_c{\eta }^{\prime }$ are around a few tens and tenths of keV, respectively. We also investigated the dependence of the ratios between these widths on the $X_2$ mass and on the $\eta$-${\eta }^{\prime }$ mixing angle, which may be good quantities for experiments. We hope that the present calculations would be checked experimentally in the future.

Comments: 9 pages, 12 figures, accepted by PRD